confusued between permutation, counting rules and factorial

The advertising director for a television show has 7 ads to use on the program. If she selects 1 of them for the opening of the show, 1 for the middle of the show, and 1 for the ending of the show, how many possible ways can this be accomplished? A doctor has three examination rooms. There are six patients in the waiting rooms. In how many different ways can patients be assigned to the examination rooms? Letters in the word ATTENDANCE are arranged in a line. How many distinct arrangements could be done if the two A's are together? In how many ways can 7 scientist be assigned to one triple and two double hotel rooms? Calculate the number of different arrangements of 5 red, 4 yellow and 3 blue bulb that can be arranged on a straight line with 12 sockets? Eleven letters in the word PROBABILITY are arranged. How many different arrangements could be done if all consonants be together? Answer: 241,920 A committee member of a conference needs to schedule a presentation of the invited speakers on the same day. The last place is reserved for one of the speakers who will be coming late to the conference. If there are five speakers, how many ways are there to schedule the presentation? Answer: 24